In the oil and gas industry, modeling of the subsurface is typically utilized for visualization and to assist with analyzing the subsurface volume for potential locations for hydrocarbon resources and well planning for field development. Accordingly, various methods exist for estimating the geophysical properties of the subsurface volume (e.g., information in the model domain) by analyzing the measurements from measurement equipment (e.g., information in the data domain). The measurements include some information of the geophysical properties that may be utilized to generate the subsurface model, such as petrophysical measurements.
The interpretation of the subsurface volume may be complicated by the rock properties within the subsurface, which is a particular problem in geomechanical modeling. Geomechanical models are a numerical representation of the state of stress and the deformation in the subsurface, which may include one or more reservoirs. The models may include various properties (e.g. density, porosity), fracture networks along with information regarding the pore pressures, stress and other mechanical properties (e.g. Young's modulus, cohesion, etc.).
By examining a few meters of core, the heterogeneity that exists at all scales in the subsurface is apparent. Sedimentary rocks exhibit heterogeneity at a range of length scales as a result of the diverse natural processes that produce sediment and disperse it as it is being deposited, and the diagenetic processes operative during subsequent burial. These differences produce materials that are compositionally and texturally heterogeneous in sedimentary successions. This heterogeneity exists both in a temporal and spatial sense over many length scales and reflects that, within genetically-related successions, sedimentary rocks are deposited as individual events (beds <0.01 m to 1 m vertical scale) that are stacked into thicker successions with related properties. Inevitably this variability in texture, fabric and composition has a direct effect on the mechanical properties of the rock. Heterogeneity on the meter scale or smaller is not typically represented in large-scale finite element models due to the number of elements that are required to realistically reproduce geologic variability in three dimensions.
Further, the recent abundance of wireline-based predictors of mechanical strength combined with scratch test technology has been utilized to predict the strength properties on the decimeter to millimeter scales. See, e.g., Suarez-Rivera, R., J. Stenebraten and F. Dagrain. 2002. Continuous Scratch Testing on Core Allows Effective Calibration of Log-Derived Mechanical Properties for use in Sanding Prediction Evaluation. In Proceedings of the SPE/ISRM Rock Mechanics Conference, Irving, 20-23 Oct. 2002. However, field scale geomechanical models are not currently capable of incorporating this level of heterogeneity.
Accordingly, a fundamental problem in geomechanical modeling involves transforming measured complexity in the subsurface to a simplified numerical model, with minimal loss of information. This process, which is referred to as upscaling, is a technique for converting a detailed geologic model to a coarser-grid simulation such that the development of stress and deformation in the two systems are comparable. Examples of elastic and plastic mechanical properties being upscaled are described in the various references, wherein the effective mechanical properties of layered solids are addressed. For example, Salamon and Backus considered the elastic strain energy and effective seismic response of a layered medium respectively. Taliercio et al. and Guo et al. examine the effective strength of a layered Mohr-Coulomb material, with special emphasis on the importance of layer orientation relative to the maximum stress, and its influence on anisotropic strength. See, e.g., Salamon, M. D, G. 1968. Elastic Moduli of a Stratified Rock Mass, Int. J. Rock Mech. Min. Sci. 5:519-527; Backus, G. E. 1962. Long-Wave Elastic Anisotropy Produced by Horizontal Layering. J. Geophys. Res. 67:4427-4440; Talierico, A., and G. S. Landriani. 1988. A Failure Condition for Layered Rock. Int. J. Rock. Mech. Min. Sci.& Geomech. Abstr. 25:299-305; and Guo, P., and F. E. Stolle. 2009. Lower and Upper Limits of Layered-Soil Strength. Can. Geotech. J. 46:665-678.
Despite these techniques, the upscaling of mechanical properties for use in a geomechanical model can fail to capture certain subsurface aspects properly. For example, standard logging tools provide estimates of petrophysical rock properties at a resolution of decimeters, and numerous predictive algorithms have been described that subsequently provide the generation of elastic-plastic mechanical properties from such wireline-based petrophysical measurements. However, these log-generated mechanical properties can be highly variable over the length scale of a single element in a geomechanical model and while petrophysical measurements reflect the gradations and heterogeneity in mechanical properties, no method exists to properly upscale the observed variability in the earth to a simplified layered model in which the upscaled mechanical units are of a tractable size for numerical simulation, and the mechanical properties assigned to these units are representative of the bulk deformation behavior of the heterogeneous material contained within them. Conventional methods for upscaling elastic and plastic mechanical properties do not properly handle upscaling of actual data. Analytic methods have been discussed in the literature to upscale a layered heterogeneous system into a representative material, but the process of upscaling all the layers into just one layer results in a loss of information. The characteristics and distribution of the deformation are not accurately represented unless some of the heterogeneity is preserved.
As the recovery of natural resources, such as hydrocarbons rely, in part, on a subsurface model, a need exists to enhance subsurface models of one or more petrophysical properties. In particular, a method of upscaling observed geologic heterogeneity into a finite number of mechanical units that can be input into numerical models is apparent. This method may utilize petrophysical data (e.g., log-data) as an input and automatically divide the subsurface into a finite number of discrete mechanical units based on the scale of the geomechanical problem being addressed. Also, a method for the upscaling of mechanical properties is needed to capture the deformation characteristics of the fully heterogeneous fine-scale model with a coarser resolution geomechanical model. That is, a need exists for a method that preserves some of the heterogeneity so that the resulting geomechanical models reasonably represent the subsurface without having to include model resolution on the order of feet.